An optimal parallel algorithm for sparse matrix bandwidth reduction on a linear array

A simple and efficient algorithm for the bandwidth reduction of sparse symmetric matrices is proposed. It involves column-row permutations and is well-suited to map onto the linear array topology of the SIMD architectures. The efficiency of the algorithm is compared with the other existing algorithms. The interconnectivity and the memory requirement of the linear array are discussed and the complexity of its layout area is derived. The parallel version of the algorithm mapped onto the linear array is then introduced and is explained with the help of an example. The optimality of the parallel algorithm is proved by deriving the time complexities of the algorithm on a single processor and the linear array.

Error-free matrix symmetrizers and equivalent symmetric matrices

A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=AprimeX. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a symmetrizer to obtain a symmetric matrix, called here an equivalent symmetric matrix, whose eigenvalues are the same as those of a given real nonsymmetric matrix is presented.

Molecular dynamics simulations on parallel and antiparallel C.G*G triplexes

Molecular dynamics (MD) studies have been carried out on the Hoogsteen hydrogen bonded parallel and the reverse Hoogsteen hydrogen banded antiparallel C.G*G triplexes. Earlier, the molecular mechanics studies had shown that the parallel structure was energetically more favourable than the antiparallel structure. To characterize the structural stability of the two triplexes and to investigate whether the antiparallel structure can transit to an energetically more favourable structure, due to the local fluctuations in the structure during the MD simulation, the two structures were subjected to 200ps of constant temperature vacuum MD simulations at 300K. Initially no constraints were applied to the structures and it was observed that for the antiparallel tripler, the structure showed a large root mean square deviation from the starting structure within the first 12ps and the N4-H41-O6 hydrogen bond in the WC duplex got distorted due to a high propeller twist and a moderate increase in the opening angle in the basepairs. Starting from an initial value of 30 degrees, helical twist of the average structure from this simulation had a value of 36 degrees, while the parallel structure stabilized at a twist of 33 degrees. In spite of the hydrogen bond distortions in the antiparallel tripler, it was energetically comparable to the parallel tripler. To examine the structural characteristics of an undistorted structure, another MD simulation was performed on the antiparallel tripler by constraining all the hydrogen bonds. This structure stabilized at an average twist of 33 degrees. In the course of the dynamics though the energy of the molecule - compared to the initial structure - improved, it did not become comparable to the parallel structure. Energy minimization studies performed in the presence of explicit water and counterions also showed the two structures to be equally favourable energetically Together these results indicate that the parallel C.G*G tripler with Hoogsteen hydrogen bonds also represents a stereochemically and energetically favourable structure for this class of triplexes.

Conformational Polymorphism in G-tetraplex Structures: Strand Reversal by Base Flipover or Sugar Flipover

Guanine rich sequences adopt a variety of four stranded structures, which differ in strand orientation and conformation about the glycosidic bond even though they are all stabilised by Hoogsteen hydrogen bonded guanine tetrads. Detailed model building and molecular mechanics calculations have been carried out to investigate various possible conformations of guanines along a strand and different possible orientations of guanine strands in a G-tetraplex structure. It is found that for an oligo G stretch per se, a parallel four stranded structure with all guanines in anti conformation is favoured over other possible tetraplex structures. Hence an alternating syn-anti arrangement of guanines along a strand is likely to occur only in folded back tetraplex structures with antiparallel G strands. Our study provides a theoretical rationale for the observed alternation of glycosidic conformation and the inverted stacking arrangement arising from base flipover, in antiparallel G-tetraplex structures and also highlights the various structural features arising due to different types of strand orientations. The molecular mechanics calculations help in elucidating the various interactions which stabilize different G-tetraplex structures and indicate that screening of phosphate charge by counterions could have a dramatic effect on groove width in these four stranded structures.

Double helix conformation, groove dimensions and ligand binding potential of a G/C stretch in B-DNA

The self-complementary DNA fragment CCGGCGCCGG crystallizes in the rhombohedral space group R3 with unit cell parameters a = 54.07 angstrom and c = 44.59 angstrom. The structure has been determined by X-ray diffraction methods at 2.2 angstrom resolution and refined to an R value of 16.7%. In the crystal, the decamer forms B-DNA double helices with characteristic groove dimensions: compared with B-DNA of random sequence, the minor groove is wide and deep and the major groove is rather shallow. Local base pair geometries and stacking patterns are within the range commonly observed in B-DNA crystal structures. The duplex bears no resemblance to A-form DNA as might have been expected for a sequence with only GC base pairs. The shallow major groove permits an unusual crystal packing pattern with several direct intermolecular hydrogen bonds between phosphate oxygens and cytosine amino groups. In addition, decameric duplexes form quasi-infinite double helices in the crystal by end-to-end stacking. The groove geometries and accessibilities of this molecule as observed in the crystal may be important for the mode of binding of both proteins and drug molecules to G/C stretches in DNA.

Conformational polymorphism in G-tetraplex structures: strand reversal by base flipover or sugar flipover

Guanlne rich sequences adopt a variety of four stranded structures, which differ in strand orientation and conformation about the glycosldic bond even though they are all stabilised by Hoogsteen hydrogen bonded guanlne tetrads. Detailed model building and molecular mechanics calculations have been carried out to investigate various possible conformations of guanlnes along a strand and different possible orientations of guanlne strands In a G-tetraplex structure. It is found that for an ollgo G stretch per se, a parallel four stranded structure with all guanines In anti conformation is favoured over other possible tetraplex structures. Hence an alternating syn-anti arrangement of guanlnes along a strand is likely to occur only in folded back tetraplex structures with antiparallel G strands. Our study provides a theoretical rationale for the observed alternation of glycosldic conformation and the inverted stacking arrangement arising from base filpover, In antlparallel G-tetraplex structures and also highlights the various structural features arising due to different types of strand orientations. The molecular mechanics calculations help in elucidating the various interactions which stabilize different G-tetraplex structures and indicate that screening of phosphate charge by counterions could have a dramatic effect on groove width in these four stranded structures.

Processing maps for hot-working of powder metallurgy 1100 Al-10 vol % SiC-particulate metal-matrix composite

The hot-working characteristics of the metal-matrix composite (MMC) Al-10 vol % SiC-particulate (SiCp) powder metallurgy compacts in as-sintered and in hot-extruded conditions were studied using hot compression testing. On the basis of the stress-strain data as a function of temperature and strain rate, processing maps depicting the variation in the efficiency of power dissipation, given by eegr = 2m/(m+1), where m is the strain rate sensitivity of flow stress, have been established and are interpreted on the basis of the dynamic materials model. The as-sintered MMC exhibited a domain of dynamic recrystallization (DRX) with a peak efficiency of about 30% at a temperature of about 500°C and a strain rate of 0.01 s�1. At temperatures below 350°C and in the strain rate range 0.001�0.01 s�1 the MMC exhibited dynamic recovery. The as-sintered MMC was extruded at 500°C using a ram speed of 3 mm s�1 and an extrusion ratio of 10ratio1. A processing map was established on the extruded product, and this map showed that the DRX domain had shifted to lower temperature (450°C) and higher strain rate (1 s�1). The optimum temperature and strain rate combination for powder metallurgy billet conditioning are 500°C and 0.01 s�1, and the secondary metal-working on the extruded product may be done at a higher strain rate of 1 s�1 and a lower temperature of 425°C.

Relationship Between The Impedance Matrix And The Transfer Matrix With Specific Reference To Symmetrical, Reciprocal And Conservative Systems

Impedance matrix and transfer matrix methods are often used in the analysis of linear dynamical systems. In this paper, general relationships between these matrices are derived. The properties of the impedance matrix and the transfer matrix of symmetrical systems, reciprocal systems and conservative systems are investigated. In the process, the following observations are made: (a) symmetrical systems are not a subset of reciprocal systems, as is often misunderstood; (b) the cascading of reciprocal systems again results in a reciprocal system, whereas cascading of symmetrical systems does not necessarily result in a symmetrical system; (c) the determinant of the transfer matrix, being ±1, is a property of both symmetrical systems and reciprocal systems, but this condition, however, is not sufficient to establish either the reciprocity or the symmetry of the system; (d) the impedance matrix of a conservative system is skew-Hermitian.

Strong metal-support interaction in Ni/TiO2 catalysts: in situ EXAFS and related studies

In situ EXAFS and X-ray diffraction investigations of Ni/TiO2 catalysts show that NiTiO3 is formed as an intermediate during calcination of catalyst precursors prepared by the wet-impregnation method; the intermediate is not formed when ion-exchange method is used for the preparation. On hydrogen reduction, NiTiO3 gives rise to Ni particles dispersed in the TiO2(rutile) matrix. The occurrence of the anatase-rutile transformation of the TiO2 support, the formation and subsequent decomposition/reduction of NiTiO3 as well as the unique interface properties of the Ni particles are all factors of importance in giving rise to metal-support interaction. Active TiO2(anatase) prepared from gel route gives an additional species involving Ni3+.

Study of voltage collapse at converter bus in asynchronous MTDC-AC systems

This paper presents the analysis and study of voltage collapse at any converter bus in an AC system interconnected by multiterminal DC (MTDC) links. The analysis is based on the use of the voltage sensitivity factor (VSF) as a voltage collapse proximity indicator (VCPI). In this paper the VSF is defined as a matrix which is applicable to MTDC systems. The VSF matrix is derived from the basic steady state equations of the converter, control, DC and AC networks. The structure of the matrix enables the derivation of some of the basic properties which are generally applicable. A detailed case study of a four-terminal MTDC system is presented to illustrate the effects of control strategies at the voltage setting terminal (VST) and other terminals. The controls considered are either constant angle, DC voltage, AC voltage, reactive current and reactive power at the VST and constant power or current at the other terminals. The effect of the strength of the AC system (measured by short circuit ratio) on the VSF is investigated. Several interesting and new results are presented. An analytical expression for the self VSF at VST is also derived for some specific cases which help to explain the number of transitions in VSF around the critical values of SCR.

Supermacroporous Polymer-Based Cryogel Bioreactor for Monoclonal Antibody Production in Continuous Culture Using Hybridoma Cells

Cryogel matrices composed of different polymeric blends were synthesized, yielding a unique combination of hydrophilicity and hydrophobicity with the presence or absence of charged surface. Four such cryogel matrices composed of polyacrylamide-chitosan (PAAC), poly(N-isopropylacrylamide)-chitosan, polyacrylonitrile (PAN), and poly(N-isopropylacrylamide) were tested for growth of different hybridoma cell lines and production of antibody in static culture. All the matrices were capable for the adherence of hybridoma cell lines 6A4D7, B7B10, and H9E10 to the polymeric surfaces as well as for the efficient monoclonal antibody (mAb) production. PAAC proved to be relatively better in terms of both mAb production and cell growth. Further, PAAC cryogel was designed into three different formats, monolith, disks, and beads, and used as packing material for packed-bed bioreactor. Longterm cultivation of 6A4D7 cell line on PAAC cryogel scaffold in all the three formats could be successfully done for a period of 6 weeks under static conditions. Continuous packed-bed bioreactor was setup using 6A4D7 hybridoma cell line in the three reactor formats. The reactors ran continuously for a period of 60 days during which mAb production and metabolism of cells in the bioreactors were monitored periodically. The monolith bioreactor performed most efficiently over a period of 60 days and produced a total of 57.5 mg of antibody in the first 30 days (in 500 mL) with a highest concentration of 115 mu g mL(-1), which is fourfold higher than t-flask culture. The results demonstrate that appropriate chemistry and geometry of the bioreactor matrix for cell growth and immobilization can enhance the reactor productivity. (C) 2010 American Institute of Chemical Engineers Biotechnol. Prog., 27: 170-180, 2011

The superheating of Pb embedded in a Zn matrix the role of interface melting

Evidence of a shape-dependent superheating of entrained nanosized Pb particles in a Zn matrix has been presented. It is shown that size dependence and pressure effects cannot explain the observed differences in melting points. The importance of crystallography and morphology at the microlevel at the interphase interface in controlling interfacial melting has been emphasized in order to explain the melting of entrained particles.

Formation of a G-quadruplex at the BCL2 major breakpoint region of the t(14;18) translocation in follicular lymphoma

The t(14;18) translocation in follicular lymphoma is one of the most common chromosomal translocations. Most breaks on chromosome 18 are located at the 3'-UTR of the BCL2 gene and are mainly clustered in the major breakpoint region (MBR). Recently, we found that the BCL2 MBR has a non-B DNA character in genomic DNA. Here, we show that single-stranded DNA modeled from the template strand of the BCL2 MBR, forms secondary structures that migrate faster on native PAGE in the presence of potassium, due to the formation of intramolecular G-quadruplexes. Circular dichroism shows evidence for a parallel orientation for G-quadruplex structures in the template strand of the BCL2 MBR. Mutagenesis and the DMS modification assay confirm the presence of three guanine tetrads in the structure. 1H nuclear magnetic resonance studies further confirm the formation of an intramolecular G-quadruplex and a representative model has been built based on all of the experimental evidence. We also provide data consistent with the possible formation of a G-quadruplex structure at the BCL2 MBR within mammalian cells. In summary, these important features could contribute to the single-stranded character at the BCL2 MBR, thereby contributing to chromosomal fragility.

New Approximation Algorithms for Minimum Cycle Bases of Graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. Although in most such applications any cycle basis can be used, a low weight cycle basis often translates to better performance and/or numerical stability. Despite the fact that the problem can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time O(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time O(n(3+2/k) ), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega) ) bound. We also present a 2-approximation algorithm with expected running time O(M-omega root n log n), a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.